Plus it's a learnt problem. We're the last generation that can remember a pre internet pre mobile phone era, where such a thing as no signal wouldn't be an issue, because there wasn't a signal to be concerned about in the first place.
Experts are idiots though. When I started (from a background of mtb like the op)I did a long run of 11 miles in my first week, 13 the week after, and 17 the week after that. Could of carried on if it wasn't for tearing my knee cartilage on the third run
"ive found I have to work very hard on a bike to get and hold a heart rate near race hm pace for even 5 minutes."
Generally your maximum HR on a bike will be lower than what you can reach running (typically ~10pbm lower). So you won't be able to maintain your running tempo HR on a bike - you need a new set of zones based on your bike max HR, or better still use power rather than HR as cougie mentioned